{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IRKO6S2SRQV5KWFWTJHMA7GWWK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8770275f14d1b7bca246bc49af00cce7bbec9ddb4abce3b47fa8315c4ed2e2b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-30T19:23:34Z","title_canon_sha256":"d9588afdf710e04a8c91bfbeb6062290958517015424a92278e3cd5c4178052c"},"schema_version":"1.0","source":{"id":"1812.00027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00027","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00027v1","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00027","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"IRKO6S2SRQV5","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IRKO6S2SRQV5KWFW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IRKO6S2S","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:f0905ac99c9da66e2c434d395a96b401e3c900f1a9c356683371e39cba0d7be1","target":"graph","created_at":"2026-05-17T23:59:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper deals with homogenization of parabolic problems for integral convolution type operators with a non-symmetric jump kernel in a periodic elliptic medium. It is shown that the homogenization result holds in moving coordinates. We determine the corresponding effective velocity and prove that the limit operator is a second order parabolic operator with constant coefficients. We also consider the behaviour of the effective velocity in the case of small antisymmetric perturbations of a symmetric kernel.","authors_text":"Andrey Piatnitski, Elena Zhizhina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-30T19:23:34Z","title":"Homogenization of biased convolution type operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00027","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:792f7b2fd2bc245f6d8ee6bb2f4bb01254146dcbfa4a73aaee93d5499f7bbdaa","target":"record","created_at":"2026-05-17T23:59:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8770275f14d1b7bca246bc49af00cce7bbec9ddb4abce3b47fa8315c4ed2e2b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-30T19:23:34Z","title_canon_sha256":"d9588afdf710e04a8c91bfbeb6062290958517015424a92278e3cd5c4178052c"},"schema_version":"1.0","source":{"id":"1812.00027","kind":"arxiv","version":1}},"canonical_sha256":"4454ef4b528c2bd558b69a4ec07cd6b2b66d204ae78d7f4afb2f7bbaf6cca1c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4454ef4b528c2bd558b69a4ec07cd6b2b66d204ae78d7f4afb2f7bbaf6cca1c6","first_computed_at":"2026-05-17T23:59:27.529553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:27.529553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/cAwJx4iVYDN7BiSGLBxdcn51cuHCpZUDvW341Q+HBX2g33kUmsWxficR0fiCmRsElHf1dnsd+UnPWn3gh0bAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:27.530061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:792f7b2fd2bc245f6d8ee6bb2f4bb01254146dcbfa4a73aaee93d5499f7bbdaa","sha256:f0905ac99c9da66e2c434d395a96b401e3c900f1a9c356683371e39cba0d7be1"],"state_sha256":"59280b672d2a688522a0e00ecd4c5c1f379201869abd8190d2b6f2cb30dee7e5"}